What makes a well-written proof? Who writes proofs well? Discussions of mathematical exposition usually revolve around larger-scale questions, such as how to organize the material, what kinds of examples to use, or how much background is necessary; by and large, around the question of what to put between the proofs. There is the art of choosing a proof, which is a subjective measure of taste. But once you’ve chosen the proof, what’s the best way to lay it out?

The style of my own proofs tends towards alternating sentences that begin with “Let” and sentences that begin with “Thus”.